Bayesian analysis for learning and updating geotechnical parameters and models with measurements - Risk and Reliability in Geotechnical Engineering - page 256

3.5

without measurements
= 2 mm
= 1 mm

Reihe3
Reihe1
Reihe2

Reihe3
Reihe1
Reihe2

σ , m
σ , m

σ ε,m = 2mm
σ ε,m = 1 mm

3

2.5

2

β

1.5

1

0.5

0

0 2 4 6 8 10 12

u x,m (mm)

Figure 5.17 Reliability index against measured displacement. Effect of measurement accuracy. (From
Papaioannou, I. and D. Straub. 2012. Computers and Geotechnics 42 : 44 - 51.)

the prior probability. Again, the difference increases with the decreasing value of σ ∈ m , because
this implies a higher information content of the measurement. A measurement that exactly
corresponds to the expected value of the deformation would lead to a posterior failure prob-
ability that is lower than the prior probability, due to a reduction of uncertainty.
For practical implementation, the reliability can be computed conditional on different
hypothetical measurement outcomes, prior to the in situ measurement. Then a threshold
value for the actual measurement may be obtained as a function of the target reliability
index β T as illustrated in Figure 5.18. Assuming that the target reliability is β T = 2.5 and
the measurement accuracy is σ ∈ m 1mm, the threshold value is 3.1 mm. Any measurement
larger than this value corresponds to a reliability index less than the acceptable one. This
would indicate that the retaining wall would not satisfy the reliability requirements at the
final excavation stage and additional measures (e.g., anchors) would be necessary.

3.5

3

β T = 2.5

2.5

2

β

1.5

1

0.5

0

0 2 4 6 8 10 12

3.1

u x,m (mm)

Figure 5.18 Reliability index against measured displacement. Measurement to comply with target reliability.
(From Papaioannou, I. and D. Straub. 2012. Computers and Geotechnics 4 2 : 44 - 51.)